Abstract
This is the first installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this first part, we exploit the synergy between the co-homological features of pure-spinor superspace and the pure-spinor zero-mode integration rules of the one-loop amplitude prescription. This leads to the study of a rich variety of multiparticle superfields which are local, have covariant BRST variations, and are compatible with the particularities of the pure-spinor amplitude prescription. Several objects related to these superfields, such as their non-local counterparts and the so-called BRST pseudo-invariants, are thoroughly reviewed and put into new light. Their properties will turn out to be mysteriously connected to products of one-loop worldsheet functions in packages dubbed “generalized elliptic integrands”, whose prominence will be seen in the later parts of this series of papers.
Highlights
This is the first part of a series of papers [1,2,3] towards the derivation of n-point one-loop correlators of open- and closed-superstring states using the pure-spinor formalism [4, 5]
Their properties will turn out to be mysteriously connected to products of one-loop worldsheet functions in packages dubbed “generalized elliptic integrands”, whose prominence will be seen in the later parts of this series of papers
+ s34P1|2|34,5,6,7 + s24P1|3|24,5,6,7 + (4 ↔ 5, 6, 7). In this first part of the series of papers [1,2,3] towards the derivation of one-loop correlators in string theory, several aspects related to the description of the massless string states via superfield kinematics have been thoroughly discussed
Summary
This is the first part of a series of papers [1,2,3] towards the derivation of n-point one-loop correlators of open- and closed-superstring states using the pure-spinor formalism [4, 5]. The second main goal of this series of papers is to find a one-loop incarnation of the duality between kinematics and worldsheet functions that results in a double-copy structure of open-superstring amplitudes [22]. The monodromies of individual terms cancel in similar patterns as the BRST variations of kinematic factors in pure-spinor superspace.2 This will be a crucial guiding principle in constructing local representations of genus-one correlators in part III and furnish a key incarnation of the duality between kinematics and worldsheet functions. Given that BRST-invariant superfields and GEIs are shown in part II to obey the same kinds of relations, the role of kinematics and worldsheet functions can be freely interchanged This generalizes the (n−3)!-term representations of tree-level correlators [14], where gaugetheory trees and Parke-Taylor factors enter on symmetric footing [20]. The final results for the correlators are quite compact
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